The contacts are part of the build-up to next week's G20 summit in Mexico, where world leaders will again attempt to agree a way through the problems.

Fears have been mounting over Spain's ability to raise funds on international markets at affordable levels.

Weaker-than-expected manufacturing and jobs data in powerhouses such as the US and China have also driven down share indexes around the globe.

In a paper for the Centre for Policy Studies think-tank, the chairman of the Treasury Select Committee, Andrew Tyrie, warned that "markets doubt the capacity of the Spanish government to service the debt".

"Among other things, they doubt whether the Spanish tax system can raise the necessary revenue while the government simultaneously engages in the deep structural reforms needed to improve productivity and secure internal devaluation.

"Without those enduring reforms, another eurozone crisis would emerge in time, even after a bailout."

He called on the IMF to ease the pressure by using the current "breathing space" to develop contingency plans for Greece to leave the Eurozone.

"Only the IMF has the necessary detachment and economic credibility to help sort out this crisis," he wrote. "These will be testing times for Christine Lagarde - her credibility, as well as that of the IMF, is on the line."

Meanwhile the Government welcomed new EU Commission plans intended to avoid future bank bail-outs as a "positive step" towards breaking the "too big to fail" culture of the European banking sector.

Under the latest proposal for EU-wide rules on bank recovery, European banks would be obliged to draw up recovery plans setting out measures they would take if the bank's financial position weakens.

They would also have to prepare a "resolution plan" with options for dealing with banks "in critical condition which are no longer viable".

EU financial services commissioner Michel Barnier said the plan would help public authorities intervene "decisively" before bank problems arise - and swiftly if they do.

"The financial crisis has cost taxpayers a lot of money" he said.

"Today's proposals are the final measure in fulfilling our G20 commitments for better financial regulation.

"We must equip public authorities so that they can deal adequately with future bank crises - otherwise citizens will be left to pay the bill, while the rescued banks continue as before knowing that they will be bailed out again".

A Downing Street spokeswoman said: "We welcome the announcement today and the proposals. The UK Government's view is it represents a positive step in tackling the problem of too-big-to-fail in the banking sector."

In last night's phone conversation Mr Cameron and Mr Obama "agreed on the need for an immediate plan to tackle the crisis and to restore market confidence, as well as a longer-term strategy to secure a strong single currency", said Number 10.

The Prime Minister has been making clear for some time that it is for the eurozone countries to take "decisive action" to stand behind their currency, said the spokeswoman.

This should involve building an effective "firewall" to prevent contagion spreading; ensuring banks are well capitalised; creating a system of fiscal burden-sharing; and enacting a supportive monetary policy across the eurozone.

The debt-ridden country has conceded that it is too big to be bailed out in the way that Greece, Portugal and Ireland were, and there are hopes that its banking restructuring fund could be allowed to tap the eurozone bail-out fund.

Its benchmark 10-year borrowing costs dropped today but were still above the 6% deemed unsustainable.

However, there are reports of a stand-off between Germany and Spain, with the eurozone's strongest economy thought to be resistant to Spain's banks directly accessing the bailout funds.

Liberal Democrat MEP Sharon Bowles said the resolution plan - not likely to come into force for years even after approval by EU governments, was likely to be overtaken by events.

"In both comedy and tragedy, timing is everything," she said.

"The proposal we have today may be useful for the future but it does not solve the current problems we face, and frankly should not be held as such. In the long-term, I have no doubt that we will want to build an effective and strong crisis resolution scheme within a pan-European framework."

The short-term required measures to force banks to develop "living wills" and make the European Banking Authority more effective.

"The European Parliament wants to embed such requirements in the capital requirements legislation on the table." said Ms Bowles.

"We cannot wait an extra two and a half years for the crisis management legislation to be negotiated and implemented - its implementation date is January 2015."

The crisis management plan highlights the fact that public authorities are badly equipped to deal with ailing banks.

Governments have so far injected "unprecedented" levels of public money into banks - the European Commission approved 4.5 trillion euros of state aid - 37% of EU GDP - between October 2008 and October 2011.

A Commission statement said: "This averted massive banking failure and economic disruption, but has burdened taxpayers with deteriorating public finances and failed to settle the question of how to deal with large cross-border banks in trouble".

European Commission president Jose Manuel Barroso said: "Two weeks ahead of the (G20) summit in Los Cabos, the Commission is presenting a proposal which will help protect our taxpayers and economies from the impact of any future bank failure.

"Today's proposal is an essential step towards banking union in the EU and will make the banking sector more responsible. This will contribute to stability and confidence in the EU in the future, as we work to strengthen and further integrate our interdependent economies."

Conservative MEP Kay Swinburne, the party's spokeswoman on economics and monetary affairs in the European Parliament, said the proposals were overdue.

"This is something which should have happened immediately after the banking crisis first arose. Failing banks were the trigger of the 2008 crisis and a mechanism for dealing with cross-border banking failures should have been thoroughly thought-out and in operation by now.

"The Commission should have concentrated on the key challenge of formulating recovery and resolution plans for banks years ago, instead of proposing politically-motivated legislation on things such as short-selling and hedge funds.

"Don't waste time rearranging the furniture when you need to make sure the roof won't fall in."